What is AEL, and how is it used?

The AEL (Automatic Exposure Lock) button is used to lock the exposure of the camera at the exposure value it sees when you press the button. It is a toggle lock/unlock button.

An example of how to use it: if your subject of interest is in the shade but the majority of the image is illuminated with sunlight, you can point the camera at the subject, press the AEL, recompose the frame, and then take the picture. The subject in the shade will be correctly exposed and the part in the sun will most likely be over exposed.
Half-pressing the shutter button also locks the exposure but that also locks the focus at the same position. With the AEL, you are free to focus wherever you want after the exposure is locked.